40. Please use the following information to answer questions 40-46:

A professor randomly selects a sample of 16 students to attend additional statistics tutoring sessions for the duration of the course. At the end of the semester, the students take a nationally standardized test of statistics knowledge. Their scores average 26 with SS = 960. The population mean on that normally distributed test is = 20. Do the data support the conclusion that the tutoring has a significant effect? Use = .05 and show all 5 steps. If significant, how large is the effect?

Step 1: Which of the following correctly represents the null and alternative hypothesis for the mentioned sample(MUST SHOW WORK FOR THIS PROBLEM)?

a. Ho: 0.05

H_1:< 0.05

b. Ho: 20

H_1:> 20

c. Ho:= 20

H_1: 20

d. Ho:> 16

H_1: 16

41. Step 2:Which of the followingrepresents the critical region for this mentioned sample(MUST SHOW WORK FOR THIS PROBLEM)?

a. t=-2.13

b. t=2.13

c. t= 2.13

d. t= 0.05

42. Compute the test statistic(t-observed)for the mentioned sample(MUST SHOW WORK FOR THIS PROBLEM).

43. Based on the calculated test statistic,would you reject the null hypothesis established in question 42 (MUST SHOW WORK FOR THIS PROBLEM)?

yes

no

44. Based on the previously conducted steps,we canconclude(MUST SHOW WORK FOR THIS PROBLEM):

a) Tutoring did not havea significant effect on exam scores

b) Tutoring reduced the exam scores

c)Tutoring had a significant effect on exam scores

d) Tutoring significantly increased exam scores.

45. Compute Cohen's d for this study(MUST SHOW WORK FOR THIS PROBLEM).

46. Interpret Cohen's d(i.e., what does it tell you about tutoring and exam scores?)

a. Cannot interpret Cohen's d meaningfully

b. Tutoring did not shift scores

c. Tutoring shifted scores down by 0.75SD

d. Tutoring shifted scores up by 0.75SD